Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

For which L(s) will be these vectors linearly dependent?

  1. Oct 24, 2011 #1
    So i have 3 vectors:
    a= [1 1 1]
    b= [2 L 0]
    c= [L 2 3]

    How do I calculate the L in order to make these vecotrs linearly dependent?

    How does ß depend from L if v= [ß 0 -1] and v is in span(a b c)?

    Thank you!
  2. jcsd
  3. Oct 24, 2011 #2


    User Avatar
    Science Advisor

    Do you know what "linearly dependent" means? Use the definition of "linearly dependent" You will get a cubic equation for L but, fortunately, there's 1 obvious root.

    For the second question, are we to assume that L is one of those values? Otherwise, the span of a, b, and c is all of R3 and [itex]\beta[/itex] can be anything.
  4. Oct 24, 2011 #3
    I guess I know.

    I wrote 3 equations:

    α + 2β + Lγ = 0
    α + Lβ + 2γ = 0
    α + + 3γ = 0

    And i got, L can be 1 or 2. Then I checked it and for these Ls the vectors are dependents. But how do I know that there aren't more Ls.

    For the second question. Yes L is from those values.
  5. Oct 24, 2011 #4
    But I maybe got the definition wrong.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook